Problem: Rewrite as a simplified fraction. ${0.1\overline{23} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 123.2323...\\ 10x &= 1.2323...\end{align*}}$ Subtracting the two equations, we have: ${990x = 122}$ ${x = \dfrac{122}{990}} $ ${x = \dfrac{61}{495}} $